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Institute for Applied and Numerical Mathematics
Junior Research Group: Numerics of PDEs
JProf. Dr. Roland Maier
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JProf. Dr. Roland Maier

  • Karlsruhe Institute of Technology (KIT)
    Institute for Applied and Numerical Mathematics
    Englerstr. 2
    76131 Karlsruhe
    Germany

Welcome on my webpage. Since July 2023, I am junior professor at the Institute for Applied and Numerical Mathematics and leader of the junior research group Numerics of PDEs. I mainly work on numerical homogenization methods for multiscale problems and on specifically designed time stepping techniques for coupled PDEs. Moreover, I am very interested in the combination of machine learning techniques and classical numerical methods.

If you are interested in writing a bachelor or master thesis in the area of Numerical Mathematics, feel free to talk to me or write me an informal email.

In the upcoming winter term 2023/24, I will give a lecture on Analytical and Numerical Homogenization. The lecture provides an introduction to homogenization methods and thus to basic concepts of my research. More precisely, the lecture is about the efficient approximation of solutions to partial differential equations if effects on multiple scales need to be taken into account. We start with elliptic equations, which will be the basis for further research questions (e.g., in a next lecture, a seminar, a master thesis, etc. if you are interested).

Current List of Courses
Semester Titel Typ
Winter Semester 2023/24 Analytical and Numerical Homogenization Lecture
Ringvorlesung Wavephenomena Lecture

Research Interests

  • Multiscale Methods
  • Numerical Homogenization
  • Semi-explicit methods for coupled PDEs
  • Discretization of (time-dependent) PDEs

Upcoming Events

Short CV

  • since JUL 2023: Junior Professor for Numerics of Partial Differential Equations, Karlsruhe Institute of Technology
  • OCT 2021 - JUN 2023: Junior Professor for Numerical Analysis, Friedrich Schiller University Jena, Germany
  • SEP 2020 - SEP 2021: PostDoc, Chalmers University of Technology and University of Gothenburg, Sweden
  • APR 2020 - AUG 2020: PostDoc, University of Augsburg, Germany
  • APR 2017 - MAR 2020: Doctoral student, University of Augsburg, Germany
  • SEP 2012 - MAR 2017: Bachelor and Master studies, University of Bonn, Germany

Awards and Prizes

  • Winner of the ECCOMAS PhD Olympiad 2021
  • Dr.-Klaus-Körper prize of the GAMM 2021
  • Kulturpreis Bayern 2020, dissertation prize
  • Appointed member of the GAMM Juniors (2020-2022)

Publications

Submitted Articles

  1. P. Lu, R. Maier, and A. Rupp. A localized orthogonal decomposition strategy for hybrid discontinuous Galerkin methods. ArXiv Preprint, 2023.
  2. D. Gallistl and R. Maier. Localized implicit time stepping for the wave equation. Arxiv Preprint, 2023.
  3. R. Altmann, R. Maier, and B. Unger. Semi-explicit integration of second order for weakly coupled poroelasticity. ArXiv Preprint, 2022.

Refereed Articles

  1. F. Kröpfl, R. Maier, and D. Peterseim. Neural network approximation of coarse-scale surrogates in numerical homogenization. Accepted for publication in SIAM Multiscale Model. Simul., 2023.
  2. Z. Dong, M. Hauck, and R. Maier. An improved high-order method for elliptic multiscale problems. SIAM J. Numer. Anal., 61(4):1918-1937, 2023.
  3. S. Geevers and R. Maier. Fast mass lumped multiscale wave propagation modelling. IMA J. Numer. Anal., 43(1):44-72, 2023.
  4. R. Maier, P. Morgenstern, and T. Takacs. Adaptive refinement for unstructured T-splines with linear complexity. Comput. Aided Geom. Design, 96:102117, 2022.
  5. F. Kröpfl, R. Maier, and D. Peterseim. Operator compression with deep neural networks. Adv. Cont. Discr. Mod., 2022, Paper No. 29, 2022.
  6. P. Ljung, R. Maier, and A. Målqvist. A space-time multiscale method for parabolic problems. SIAM Multiscale Model. Simul., 20(2):714-740, 2022.
  7. R. Maier and B. Verfürth. Multiscale scattering in nonlinear Kerr-type media. Math. Comp., 91(336):1655-1685, 2022.
  8. R. Altmann and R. Maier. A decoupling and linearizing discretization for weakly coupled poroelasticity with nonlinear permeability. SIAM J. Sci. Comput., 44(3):B457-B478, 2022.
  9. R. Maier. A high-order approach to elliptic multiscale problems with general unstructured coefficients. SIAM J. Numer. Anal., 59(2):1067-1089, 2021.
  10. R. Altmann, R. Maier, and B. Unger. Semi-explicit discretization schemes for weakly-coupled elliptic-parabolic problems. Math. Comp., 90(329):1089-1118, 2021.
  11. A. Caiazzo, R. Maier, and D. Peterseim. Reconstruction of quasi-local numerical effective models from low-resolution measurements. J. Sci. Comput., 85(1), Article No. 10, 2020.
  12. R. Altmann, E. Chung, R. Maier, D. Peterseim, and S.-M. Pun. Computational multiscale methods for linear heterogeneous poroelasticity. J. Comput. Math., 38(1):41-57, 2020.
  13. P. Hennig, R. Maier, D. Peterseim, D. Schillinger, B. Verfürth, and M. Kästner. A diffuse modeling approach for embedded interfaces in linear elasticity. GAMM-Mitteilungen, 43(1):e202000001, 2020.
  14. S. Fu, R. Altmann, E. Chung, R. Maier, D. Peterseim, and S.-M. Pun. Computational multiscale methods for linear poroelasticity with high contrast. J. Comput. Phys., 395:286-297, 2019.
  15. R. Maier and D. Peterseim. Explicit computational wave propagation in micro-heterogeneous media. BIT Numer. Math., 59(2):443-462, 2019.
  16. C. Paulus, R. Maier, D. Peterseim, and S. Cotin. An immersed boundary method for detail-preserving soft tissue simulation from medical images. In: P. Nielsen, A. Wittek, K. Miller, B. Doyle, G. Joldes, and M. Nash, editors, Computational Biomechanics for Medicine, MICCAI 2017, pp. 55-67. Springer, Cham, 2019.

Articles in Collections

  1. P. Hennig, M. Kästner, R. Maier, P. Morgenstern, and D. Peterseim. Adaptive isogeometric phase-field modeling of weak and strong discontinuities. In: J. Schröder and P. Wriggers, editors, Non-standard Discretisation Methods in Solid Mechanics, volume 98 of Lecture Notes in Applied and Computational Mechanics, pp. 243-282. Springer, Cham, 2022.

Articles in Proceedings

  1. R. Altmann, R. Maier, and B. Unger. A semi-explicit integration scheme for weakly-coupled poroelasticity with nonlinear permeability. Proc. Appl. Math. Mech., 20(1):e202000061, 2021.
  2. A. Caiazzo, R. Maier, and D. Peterseim. Reconstruction of quasi-local numerical effective models from low-resolution measurements. Oberwolfach Reports, 16(3):2149-2152, 2019.
  3. R. Maier and D. Peterseim. Fast time-explicit micro-heterogeneous wave propagation. Proc. Appl. Math. Mech., 18(1):e201800294, 2018.

Theses

  1. R. Maier. Computational Multiscale Methods in Unstructured Heterogeneous Media. Doctoral Thesis, University of Augsburg, 2020.
  2. R. Maier. Simulation of Elastic Deformation by the Immersed Boundary Method. Master Thesis, University of Bonn, 2017.
  3. R. Maier. Die Space-Time-DG-Methode: Theorie und Numerik für parabolische Gleichungen in einer Dimension. Bachelor Thesis, University of Bonn, 2015. In German.